Computer Science > Logic in Computer Science

Abstract: We investigate the Constraint Satisfaction Problem (CSP) over templates with
a group structure, and algorithms solving CSP that are equivariant, i.e.
invariant under a natural group action induced by a template. Our main result
is a method of proving the implication: if CSP over a coset template T is
solvable by an equivariant algorithm then T is 2-Helly (or equivalently, has a
majority polymorphism). Therefore bounded width, and definability in
fixed-point logics, coincide with 2-Helly. Even if these facts may be derived
from already known results, our new proof method has two advantages. First, the
proof is short, self-contained, and completely avoids referring to the
omitting-types theorems. Second, it brings to light some new connections
between CSP theory and descriptive complexity theory, via a construction
similar to CFI graphs.